雙語科技百科(數學) 第34期:負數的使用
The Use of Negative Numbers
The introduction of negative numbers is a great contribution to mathe-matics by ancient Chinese Nine Chapters on the Mathematical Art(Jiuzhang Suanshu)，negative numbers were used in the eighth chapter on solving systems of simultaneous equations. For instance, revenue num-bers are considered positive，while expense numbers are deemed negative;or sur-plus amounts are viewed as positive，while deficit amounts are seen as a problem calculating grains，the increased grains are considered positive，and the lost grains，negative. At the time，calculation was done by the method of Suan Chou(counting rods)Red rods were used to denote positive coefficients，and black ones to denote negative ones. Or in another case，the normal position of Su-an Chou denoted positive，while an inclined position denoted negative.
負數的引進，是中國古代數學家對數學的一個巨大貢獻。在《九章算術》的第八章“方程”中，就引人了負數解聯立方程組。如負數出現在方程的係數和常數項中，把“賣(收人錢)”作爲正，則“買(付出錢)”作爲負，把“餘錢”作爲正，則“不足錢”作爲負。在關於糧谷計算的問題中，是以益實(增加糧谷)爲正，損失(減少糧谷)爲負等。當時是用算籌來進行計算的，以紅籌爲正，黑籌爲負；或將算籌首列作正、斜置作角。Rules for the calculation of signed numbers were also given in Jiuzhang rding to the book, the deduction(or subtraction)of two numbers with the same sign(from another number) equals the deduction of the absolute values of the two numbers，while the deduction of two numbers with different signs equals the addition of the absolute values of the iwo numbers. Also一a positive number subtracted from zero gives a negative number,whereas a negative num-ber subtracted from zero gives a positive number. The addition of two numbers with different signs equals the deduction of their absolute values，while the addition of iwo numbers with the same sign equals the addition of their absolute plus a positive number is still a positive number,and zero plus a negative number is still a negative number. Until the 17th century，it was the most complete depiction on the rules for adding and subtracting positive and negative一 numbers in the world.
在《九章算術》中，除了引進正負數的概念外，還完整地記載了正負數的運算法則:同號兩數相減，等於其絕對值相減;異號兩數相減，等於其絕對值相加;零減正數得負數，零減負數得正數。異號兩數相加，等於其絕對值相減;同號兩數相加，等於其絕對值相加;零加正數得正數，零加負數得負數。直到公元17世紀以前，這還是正負數加減運算最完整的敘述。
Negative numbers appeared very late in the noted mathemati-clans did not admit negative numbers，because they consider zero as“nothing”and could not understand that something could be even less than“nothing，”and so considered negative numbers“absurd.”It was only in the 17th century when Descartes invented the coordinate system，which gave a geometrical explanation and an actual meaning for negative numbers，that negative numbers began to be accepted gradually.
在西方，負數出現得很晚。許多著名數學家一直不承認負數。他們把零看作“沒有”，他們不能理解比“沒有”還要“少”的現象，因而認爲負數是“荒謬的”。直到17世紀，笛卡兒創立了座標系，負數獲得了幾何解釋和實際意義，才逐漸得到了公認。The introduction of negative numbers is an important contribution of Chinese mathematicians to world mathematics. With the introduction of negative numbers，the whole numbers and rational numbers became complete.
負數的引進，是中國古代數學家貢獻給世界數學的一份寶貴財富。負數概念引進後，整數集和有理數集就完整地形成了。
